12.9.45 problem 39 part(c)

Internal problem ID [1801]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 39 part(c)
Date solved : Monday, January 27, 2025 at 05:35:12 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve((2*x+1)*(diff(y(x),x)+y(x)^2)-2*y(x)-(2*x+3)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{2 x} x +{\mathrm e}^{2 x}-c_1}{{\mathrm e}^{2 x} x +c_1} \]

✓ Solution by Mathematica

Time used: 0.373 (sec). Leaf size: 41

DSolve[(2*x+1)*(D[y[x],x]+y[x]^2)-2*y[x]-(2*x+3)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{2 x+1} (x+1)-c_1}{e^{2 x+1} x+c_1} \\ y(x)\to -1 \\ \end{align*}